Simplify the following expression: $ n = \dfrac{2}{7} + \dfrac{-8a + 1}{2a + 8} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2a + 8}{2a + 8}$ $ \dfrac{2}{7} \times \dfrac{2a + 8}{2a + 8} = \dfrac{4a + 16}{14a + 56} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-8a + 1}{2a + 8} \times \dfrac{7}{7} = \dfrac{-56a + 7}{14a + 56} $ Therefore $ n = \dfrac{4a + 16}{14a + 56} + \dfrac{-56a + 7}{14a + 56} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{4a + 16 - 56a + 7}{14a + 56} $ $n = \dfrac{-52a + 23}{14a + 56}$